ISO2002: an analytical stochastic model of multi-difference GPS carrier-phase data |
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Authors: | Email author" target="_blank">C -D?ZhangEmail author X -P?Wu J -M?Hao H -B?He D -M?Zhao |
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Institution: | (1) Institute of Geodesy and Geophysics, Chinese Academy of Science, Wuhan, 430077, China;(2) Department of Geodesy, Zhengzhou Institute of Surveying and Mapping, Longhai Middle Road No. 66, Zhengzhou, 450052, China |
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Abstract: | The differencing technique is useful in global positioning system (GPS) positioning when two or more GPS receivers collect simultaneous observables from common satellites at each epoch, and all carrier-phase observables have the same normal distribution. An analytical probability distribution of the single-, double-, triple- and multi-difference GPS observables is obtained. This analytical model, called ISO2002, has a good matrix structure, in which I indicates the number of receivers, S indicates the number of observed satellites, and O indicates the number of epochs. The variance–covariance matrix can be expressed as the Kronecker product of several small matrices, so its inverse is equal to the Kronecker product of the inverses of these sub-matrices. Moreover, these small matrices are circulant or symmetric diagonal Toeplitz matrices, so their inverses have analytical solutions. The analytical model ISO2002 proposed to compute the inverse variance–covariance matrix is shown to be very effective. |
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Keywords: | GPS Double Difference multi-difference Variance covariance matrix Matrix inversion Toeplitz matrix Kronecker product Analytical inverse |
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